A377712 a(n) is the least divisor of n with as many decimal digits as n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 10, 31, 16, 11, 17, 35, 12, 37, 19, 13, 10, 41, 14, 43, 11, 15, 23, 47, 12, 49, 10, 17, 13, 53, 18, 11, 14, 19, 29, 59, 10, 61, 31, 21, 16, 13, 11, 67

Offset

1,10

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

1 <= n/a(n) <= 9.

Example

For n = 42: the divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42; the least divisor with 2 digits is 14, so a(42) = 14.

Maple

f:= proc(n) local d, t;
  t:= ilog10(n);
  min(select(d -> ilog10(d)=t, numtheory:-divisors(n)))
end proc:
map(f, [$1..100]); # Robert Israel, Nov 06 2024

Mathematica

s={}; Do[m=0; d=Divisors[n]; Until[Length[IntegerDigits[d[[m]]]]==Length[IntegerDigits[n]], m++]; AppendTo[s, d[[m]]], {n, 67}]; s (* James C. McMahon, Nov 06 2024 *)

Prog

(PARI) a(n, base = 10) = { my (w = #digits(n, base)); forstep (x = base-1, 1, -1, if (n%x==0 && #digits(n/x)==w, return (n/x); ); ); }
(Python)
def A377712(n): return n//next(d for d in range(n//10**(len(str(n))-1), 0, -1) if not n%d) # Chai Wah Wu, Nov 06 2024

Crossrefs

Cf. A055642, A109940.

Sequence in context: A305947 A100830 A180176 * A350494 A168100 A088475

Adjacent sequences: A377709 A377710 A377711 * A377713 A377714 A377715

Keyword

nonn,base,easy

Author

Rémy Sigrist, Nov 04 2024

Status

approved